In recent years, Navy Navigational Satellites have been operating
at temperatures Some 20° to 30° F higher than were predicted from
preflight tests and calculations. Therefore , an exhaustive analysis
of the thermal design was conducted, which was followed by a very
extensive thermal vac~um testing program 'to aid in correcting this
situation. The testing program verified most of the a,nalysis and
supplied answers to problems that could not be answered in the analysis.
As a result of both the analysis and the testing program, the difference
bet ween orbital results and preflight calculations has been reduced
to a range of from 2° to 3° F .
S. E. Willis, Jr.
THERMAL
F
or the past two years, signals transmitted by
orbiting satellites developed by the Applied
Physics Laboratory have provided the Navy with
an accurate, world-wide navigational system. However, realizing that such a system is never completely perfected, APL has sought to achieve improved satellite performance and to extend the
useful life of the satellites' electronic equipment.
These objectives were found to be attainable if the
interior temperature of the individual satellites
could be maintained at a constant and mild level.
The operating temperature of a satellite is determined by the balance between the internally generated power, the externally absorbed power from
the sun and the earth, and the rate at which heat
is emitted from the satellite to free space. The
18
balance is a delicate one-a change of 5 % in the
absorbed power level would cause the internal
temperature of the satellite to change by 15 ° to
20 ° F , and a change of 5 % in internal power dissipation would cause the internal temperatures to
change by 6 ° to 8 ° F.
The direct solar input is generally the largest
heat source. As the earth rotates about the sun, the
angle between the earth-sun line and the plane
of the satellite's orbit changes, causing the fraction
of time the satellite spends in the earth's shadow to
vary. Although the thermal capacity of the satellite
is generally sufficient to keep the internal temperature from changing more than 2° to 4 ° F during a
single orbit, the total heat absorbed in a minimumsunlight orbit is 70 % or less of that which is absorbed when the satellite is illuminated all of the
.\PL Technical Digest
tlESIGN 01
CURRENT NAVIGATIONAL SATELLITES
time. The variation in the intensity of the sunlight
caused b y the seasonal variation in the di stance
f rom the earth to sun a nd the increase in the
amount of h eat a bsorbed over the useful life of
the satellite caused by d egradation of the exterior
paint with utraviolet degradation combine to cause
a n additiona l varia tion of 40 o/c to 50 % in the
am ount of h eat absorbed from the sun.
I t is clear then tha t the desired na rrow band of
acceptable operating temperatures cannot be
achieved b y passive means. Accordingly, a thermostatically controlled h eating system was devised .
The individual resistive h ea ters attached to the
components are powered b y the solar array and
controlled by mercury thermostats. The goal of the
thermal d esign is to use available amounts of solar
array po\\'er in the coldest case and a lmost none in
November-December 1966
the hot case to maintain the critical satellite components in the ra nge of 60 ° to 70 ° F.
Data are now being received from satellites v\lith
this a utomatic tempera ture control (ATe ) system
d esign , which indicates they are performing very
well. The difference between prelaunch predictions
of tempera tures and the tempera tures actua lly
achieved in orbit is much less than for a ny other
satellites design ed a t APL. The critica l components,
which are the power system batteries, their associated zener diod es, and the elec tronic "book"
packages, h ave been h eld between 63 ° and 73°Fa range that should extend the life of the m emory
and power systems. This a rtirledescribes the methods of designing the h eat flow system to achieve
these results.
The thermal design of a satellite involves d esign
19
of the external paint scheme, the provision of sufficient heating capacity, and the design of suitable
heat transfer paths to utilize efficiently the available
automatic temperature control power. To minimize
solar heating, the satellite body was painted white.
For precise temperature control it was decided
that heaters with individual thermostats would be
placed directly on each of the components requiring constant temperature. This called for 16 heating units for each satellite. The conductive heat
flow paths were controlled by the proper selections
of spacer materials between the inner and outer
structures. The radiative heat flow paths were
controlled by the selection of the number of layers
of aluminized mylar between the inner components
and the outer structure.
Heat Sources
The internally generated heat of the satellite
consists of heat generated by the electronics and
the thermostatically controlled heater output. The
heat sink is the exterior of the satellite.
The major contributors of heat are the oscillator,
located in the thermally isolated center structure
of the satellite; the electronic "books," located in
four quadrants around the center structure; the
power system batteries, located between the book
quadrants; and the transmitters and voltage regulator, mounted on the bottom or baseplate of the
satellite.
The heat output of the oscillator is nearly constant. The outside temperature of the oscillator is
not critical since satisfactory operation is attained
over a range of 50° to 120° F.
The book heat dissipation is nearly constant, but
most effective operation is attained when the temperature variation is only 10° to 15°F.
The battery heat output is the most unpredictable, and the temperature requirements are the
most critical of any in the satellite. The heat output is influenced by battery efficiency and therefore by battery temperature, and by the charging
cycle. This charging cycle is influenced by the
portion of time per orbit that the satellite is in
the earth's shadow; by the seasonal variation in
the intensity of the sun; by the azimuth angle of
the solar blades relative to the plane of the orbit;
and by the degradation of the solar cells on the
solar blades.
The dissipation of the transmitters is approximately constant, and that of the voltage regulator
is dependent upon the power system. However, the
allowable operating temperature range of the transmitters and voltage regulator is very wide so that
20
the only effect of variations in voltage regulator
dissipation is the effect that it has on the temperature of the baseplate.
The heating units are controlled by mercury
thermostats that close when the temperature is
below 70°F and open when the temperature is
above 70 ° F.
Heat Transfer Paths
Heat is transferred between components and
from the interior to the exterior of the satellite by
both radiation and conduction and is dissipated
frem the external surfaces by radiation into space.
Paths for heat flow exist through the electronic
components themselves and through their supporting structures. Detailed methods of solving for
resistance to heat flow are given in the following
sections. Where it was not possible to determine
resistances an.alytically, vacuum thermal mock-up
tests were conducted.
Heat flow paths are dictated by the structure of
the satellite; however, several paths can be varied
by the designer to provide the desired temperature
control. Figure 1 is a schematic diagram which
shows the thermal paths in the satellite between
the various heat sources and the outside shell. The
thermal resistances shown in the shaded areas in
Fig. 1 are made of suitable material. Where highly
conductive paths are desired, soft aluminum slugs
are used. For higher thermal resistance, G-10 epoglass is used. In addition, the depth of multilayer
thermal insulation between the inner structure and
the outer shell can be adjusted to meet heat flow
requirements. The general philosophy adopted was
to make the conductive resistances as low as possible and to control the overall internal to external
resistance with the number of layers in the multilayer radiation insulation blanket.
Optimum values of the resistances could not be
determined directly. Numerous vacuum thermal
mock-up tests were not advisable although this
method could be used to check the design. A
practical method had to be devised to determine
the values of the variable resistances, which would
provide satisfactory temperature control under all
possible orbit conditions. An electrical analog of
the heat-:-flow system was therefore constructed,
using values for the heat transfer paths determined
as described below. The model was corrected and
refined in accordance with results from vacuum
thermal mock-up tests. The best values for the
variable resistances could then be determined by
using the model to simulate all possible conditions
of satellite orbit.
APL Technical Digest
Fig. I-Schematic diagram showing basic thermal
conduction paths, within satellite. (Only one quadrant of the satellite is shown.)
Conduction Paths
The basic thermal conduction paths of the satellite are shown in Fig. 1. The values of the thermal
resistances with the exception of Fl, F2, and F3,
were more or less dictated by structural considerations. The uncertain resistance between members
was greatly reduced by using silicone grease, indium
foil, and as many fasteners as practical. Still the
assumption of zero thermal resistance across the
joints caused the analysis to be slightly in error
when compared to thermal vacuum tests of the
satellites.
The thermal resistance of the connections Fl, F2,
and F3 between the satellite interior and exterior
which consist of spacer material in parallel with
metallic screws, could be selected at will. The F3
resistances provide the path for dissipation of internal pmver through the "baseplate." The Fl and
F2 resistances link the various parts of the internal
structure to the "shell." To achieve the design goal
of using all available automatic temperature control power in the cold case, it was necessary to make
the Fl and F2 spacers as conductive as possible.
This and the use of low radiation resistance
material also allowed the satellite to operate at the
desired temperatures in the cases where the exterior
\\ as hot. The use of soft aluminum as spacer
material provided a satisfactorily low resistance as
was verified by later analog tests.
The baseplate is the metallic plate on the bottom
of the satellite body where the satellite is mounted
to the rocket during launch. The shell is that por·
Novembe1"-December 1966
tion of the satellite body consisting of the top, side,
and the epo-glass portion of the bottom.
Fortunately, all of the internal structural members were formed from sheet metal with approximately constant cross-section. It was therefore
possible to construct an electrical analog of the
thermal situation by cutting analogous blank patterns out of teledeItos paper, an electrically conductive material commonly used in analog field plotter
work. Heat which is conducted from one isothermal
area (a node) to another is exactly analogous to
an electrical charge which is conducted from one
equipotential area to another. If the shapes and
contact areas of the teledeItos paper duplicate those
of the sheet metal the electrical resistances of the
paper will simulate exactly the thermal resistances
of the metal.
It v,as not possible to obtain analytically the
conductive or radiative resistance between shell and
baseplate or that between the inside and the outside of the shell. These resistances were obtained
during thermal vacuum testing of a thermal
mock-up of the satellite as discussed below.
To simplify the conductive and radiative resistance diagram, tv,o important assumptions were
made.
1. The temperature of each of the four battery
stacks is equal to the average battery temperature.
2. The temperature of each of the four book
quadrants is equal to the average book temperature.
With the use of these assumptions and the customary a-v network transformations, the network of
Fig. 1 reduces to that of Fig. 2.
Fig. 2-Reduced conductive paths.
Internal Radiative Paths
The radiation heat transfer paths were of
necessity evaluated by two different methods. It
was possible to use a standard analysis to determine
the radiation resistance between the books, bat-
21
teries, center structure, and the inside layer of the
multilayer insulation. This was done by first determining the black-body exchange coefficients, "FA,"
using an available computer program, "CONFAC
II," then converting these to gray-body exchange
coefficients, "Script FA," and multiplying by the
cubic M ij = (Ti 2 + T /) (Ti + T j ), which is obtained from factoring T i - T j from T i 4 - T/. The
procedure is as follows:
tive paths with a correction of t,.M ij when the
temperatures change by !:lTi or t,.T j •
27.6/ M
11.1 7IM
I S.I / M
Q BOOKS,
_ _ I\JV~"""-~~,.-___
Since
Q BOOK ATC
R SH El l
MULTILAYER
INSULATJON
R= t,.T
Q'
and
then
R = cr 9!A (TI 2 + T 22 ) (Tl
where Q
T 1,
+ T 2)
,
= heat flow
R = thermal resistance
cr = Stefan-Boltzmann constant
T2 = absolute temperatures of the areas in
Fig. 3-Comhined radiation and conduction paths.
question, and
9! A
= 1.-(1_ 1) = _1 + ~(~ _ 1) ,
Al El
FA
A 2 E2
where Al = area at temperature Tl
A 2 = area at temperature T 2
El = infrared emissivity of Al
E2 = infrared emissivity of A 2 , and
FA =
cos Al cos A2 dA 1dA 2
l122
Al
A;!
where ll'2 = line connecting dA 1 and dA 2
Al = angle between l1 2 and the normal to
dA 1
A2 = angle between l12 and the normal to
dA 2 •
If If
Another approach was needed for the radiation
resistance through the insulation to the shell. Because of the many holes in the multilayer insulation,
it was not possible to calculate the resistance
through it more closely than an order of magnitude.
Vacuum thermal testing was used to determine the
value of the combined conduction and radiation
resistance as a function of depth of insulation.
The combined radiation and conduction paths
are shown in Fig. 3. For a first trial it is possible
to treat radiation and conduction resistances in the
same manner. To avoid unwieldly numbers in
Fig. 3, the radiation resistances that are shown use
the parameter M = M i j X 10-6 • This procedure
allows the radiation paths to be treated as conduc-
22
Exterior Thermal Design and
Thermal Coatings
.
The exterior of the satellite is composed of three
general areas: I (shell) , II (baseplate ) , and III
(solar blades). The temperatures of these three
areas are a function of the conduction and radiation resistances between them, as well as the
external direct solar, earth-reflected solar, and
earth-emitted energy rates, and the internally
dissipated power of the satellite. The temperature
of each area is that temperature at which the
emitted energy rate of the area equals the input
energy rate to that area.
The three steady-state temperatures of these'
regions are obtained from the three simultaneous
equations generated by considering the shell, baseplate, and solar blades as closed systems.
AREA I (SHELL ) -The heat input to the shell
will be the sum of the radiation from solar blades
to shell, conduction from solar blades to shell, conduction from baseplate to shell, absorbed solar
energy, absorbed earth-reflected solar energy, and
absorbed earth-emitted infrared radiation. This
can be expressed mathematically as
Q in = (K R) SB-SH(TSB4 - T SH4)
(KC)SB-SH(T sB - T SH) +
(KC)BP-SH(T BP - T SH)
+ Gs L P ASnlX n + reGs
+
n
L FreseAnlXn + ( KR)
E-I'm
(T,,;4 - T SII ) 4
n
APL Technical Digest
On the other hand, the heat output can only be
the radiation from the shell to free space:
Q ou t
= (KR) SH-sp(TsH4 -
Subscripts:
R = Radiation
C = Conduction
E = Earth
BP = Baseplate
SH = Shell
SB = Solar blades
SP = Space.
0),
which at equilibrium will equal the heat input.
AREA II (BASEPLATE ) - The thermal input to
the baseplate will be the sum of the internal satellite heating, the solar energy absorption, and the
heating caused by absorption of earth-reflected
sunlight:
Q in = I.P.
+ GsOt.BPPAS BP + reGSOt.BP
Lrn Fre 3eA rn .
The heat leaving the baseplate will be the sum of
the energy conducted from baseplate to shell, radiation to space, and radiation to the earth:
Qout
= (Kc ) BP-SH(T BP -
T SH )
(K R ) BP_SH(TBp4 - 0 ) +
(K R ) BP_E(T Bp4 - T E4) ,
+
which at equilibrium will be equal to the heat
input.
There is no direct radiation or conduction
coupling between the solar blades and the baseplate. The net radiation and conduction between
baseplate and shell is accounted for in the
term containing the experimentally determined
(Kc) BP-SH'
There is no way to solve these equations for
T SH, T BP, and T SB without involving as many as
15 nonphysical solutions containing imaginary and
negative absolute temperatures for each. An iteration process can be used to obtain the solutions to
the desired accuracy.
If we let
AREA III (SOLAR BLADEs ) - Heat input to the
solar blades will be the sum of the heat absorbed
from the sun and the absorbed earth-reflected sunlight:
Q in = GsOt.sBPAS SB + reGSOt.SB
L
FreseA r .
T SH = Txo + XO
T BP = Tyo + Yo
T SB = T Zo + Zo ,
then
r
T SH4
TBP4
T SB4
The heat output from the solar blades will be
the sum of the infrared radiation to the earth, the
heat conduction to the shell, infrared radiation to
the shell, and radia tion to space:
Q out = (K R )SB-E(T sB4 - T E4) +
(K C)SB-SH(T sB - T SH) +
(K R )SB-SH(T sB4 - T SH4) +
(K R)SB-Sp(T sB4 - 0) ,
and at equilibrium will be equal to the heat input.
Term definitions for the foregoing equations are:
(K R ) = Coefficient of radiation heat transfer
(K c ) = Coefficient of conductive heat transfer
(I.P.) = Internal satellite power which is dissipated through the baseplate
PAS = Projected area to the sun
re = Earth's albedo (percent of incident solar
power which is reflected by the earth)
Frese = View factor of a satellite panel to the
sunli t portion of the earth
T = Temperature in degrees R
Q = Heat flow
A = Area
Gs = Solar constant
Ot. = Percent of incident solar energy rate
which is absorbed.
N ovember-December 1966
~
~
~
TX04 + 4Tx 03 x o
T y0 4 + 4T y0 3 yo
Tz 04 + 4T z0 3 Zo .
These approximations are substituted in Areas
I, II, and III to form three new simultaneous
linear equations in Xo, Yo, and Zoo Initial values of
Tx o, Tyo, and Tz o are assumed, and the appropriate
projected area to the sun (PAS) values for the
orbital position under consideration and appropriate values of Ot.n,t/I ,r are substituted for the paint
pattern under consideration, in this case all white.
Values of Xo, Yo, and Zo are then calculated, and
new values of T x, T y, and T z are obtained:
TX1
= Txo + Xo;
TY1
= Tyo + Yo;
T Z1 = T zo + Zoo
The following substitutions are made:
Txo ~ Tx 1; Tyo ~ TY1; Tz o ~ Tz 1; Xo ~ Xl; Yo
Y1; Zo~ Zl'
These are used to solve for Xl' Y1, and Zl' This
process converges to x n, Yn, Zn < 0.5°F very rapidly
provided that suitable values are chosen for Tx o,
Yo, and Zoo
~
System Analog and Thennal Mock-up
The thermal resistances shown in Fig. 3 are
23
then put on an electrical analog device using the
following analogy:
Current (10 rna) ~ (1.0 watt heat flow)
Potential Difference (100 mv) ~ 1°F
Resistance (10 ohms) ~ 1 of/ watt.
The electrical analog device consisted of constant
voltage power supplies to maintain voltage levels
corresponding to calculated temperatures at the
shell and baseplate reference nodes; constant-current power supplies to supply current at the book,
battery, and oscillator nodes corresponding to the
heat inputs at these points; and decade resistors
with a resistance proportional to the thermal resistances between nodes.
As was discussed above, four thermal resistances
could not be obtained analytically. Consequently,
various calculated shell and baseplate temperatures
were set on a thermal mock-up of the satellite in
thermal vacuum tests. The heat inputs to the batteries, books, and oscillators were recorded along
with their temperatures. This information was
used to determine the thermal resistance through
the multilayer insulation to the shell and baseplate, the resistance across the shell, and the resistance between shell inside and baseplate.
Prior to the thermal mock-up thermal vacuum
tests, with these resistances unknown, it was not
possible to know exactly how much of the power
dissipated by books, batteries, and oscillator went
to the shell and how much went to the baseplate.
The steady-state temperatures of the shell and
baseplate are proportional to the fourth root of
the total heat flow, Q, into the node (internal plus
external) and are inversely proportional to the
fourth root of the area of the shell or baseplate.
The shell area is so large that the change in shell
temperature per watt of internal dissipation is less
than 1°F and can be neglected. However, the
change in baseplate temperature per watt of internal dissipation is of the order of 3° to SOF.
Neglecting changes in baseplate temperature causes
predicted internal temperatures to be notably lower
than orbital results. The change in baseplate temperature is accounted for in the analog (Fig. 3)
by setting up a baseplate reference and assuming a
resistance between it and the baseplate. The value
of this resistor is set to correspond to 1 of/ watt.
When the baseplate reference is set to a potential
corresponding to the baseplate temperature assuming no dissipation of internal power, the current
from books, batteries, and oscillator (corresponding to heat flow) which passes through the baseplate node to the baseplate reference node causes
a potential difference between these nodes. This
24
potential difference corresponds to the temperature
increase in the baseplate caused by internal power
dissipation, and therefore the baseplate potential
corresponds to the actual baseplate temperature.
With this model the temperatures of the internal
nodes were established over the range of conditions expected in orbit. It was then possible to
evaluate temperature dependence in the radiation
resistances with the relationship,
Mij
= (Ti + T/) (Ti + T j ) .
2
Book-to-battery resistances and baseplate referenceto-baseplate resistances were found to vary with
temperature as given in Fig. 4. All other resistances
were found to be reasonably insensitive to temperature, and radiation resistances could therefore be
added to conduction resistances. The final analog
for the whole satellite was then completed as shown
in Fig. S.
5.5,------.- - -- - . - - - - , - - - - . - - - - ,
BASEPLATE-BASEPLATE REF
RESISTANCE VS TllP
4.5 f----+~..".--+----+_---+---_l
~
-......
~
cz
3.51-----+---+----f:!oooooo;;::---+---_l
2.5 L.-_ _--1._ _ _- L_ _ _L -_ _---l._ _ _-J
-20
80
20
40
60
o
1.5 , - - - - - - - . " . . - - - - - . - - - - , - - - - - - , - - - - ,
1.4
'"
~
cz
~
1.3
1.2
50
60
70
80
90
100
Fig. 4-Variable resistances for analog.
Conclusions and Results
The analog shown in Fig. S is capable of predicting book, battery, and oscillator temperatures
to approximately ± 1 OF when compared to thermal
vacuum test results. The only significant revision
made to the analytically obtained analog for agreement with thermal vacuum test results was in the
books-to-battery resistance. This lack of agreement
is attributed to poor conductance through the joints
APL Technical Digest
Q BOOK ATC
"'--.JVV'\",;.,.;"';"-iIj~-
Q BOOKS
never in the earth's shadow throughout the orbit,
the automatic temperature control power approached zero while the battery temperature rose
to 72°F. This indicates that the automatic temperature devices are functioning as designed.
BASEPLATE ...--~v---.
BASEPLATE REF.
OUTSIDE SHELL
Fig. 5 - Final flight hardware analog.
between individual books and to the complicated
heat paths through the books. All other changes in
the analog were negligible.
Having a good mathematical model (the analog), it was possible to determine the effect on
temperature of variations in orbit which were unanticipated before launch; it was possible to see
what changes if any were required in the satellite
to meet the design goals; and it was possible to
anticipate the effect on temperature and on the
requirements for automatic temperature control
power of changes in design of components in future
sa telli tes.
The predicted temperatures of the satellite under
various orbital conditions are shown in Table 1.
For comparison purposes, the orbital temperatures for the baseplate and batteries are shown in
Fig. 6 and for the oscillator and books in Fig. 7.
Baseplate temperatures are almost entirely within
the calculated range. The oscillator orbital temperatures are almost exactly equal to the thermal
vacuum values, but the expected increase caused
by seasonal variations in the solar constant failed
to materialize. The predicted oscillator temperatures are therefore approximately 2Y2 OF too high.
The book temperatures are approximately 112° to
2°F higher than the predicted values while the
battery temperatures are approximately 12 OF too
high.
On the first satellite built to this design, orbital
telemetry has indicated that almost all available
automatic temperature control power was used
shortly after launch during the random tumble
phase while maintaining the batteries at 67°F.
Later, as the satellite made the transition to an
orbital confi.g uration such that the satellite was
Novembe1'-December 1966
W INTER
SOLSTICE
Fig. b--Comparison of predicted and orbital temperatures for baseplate and batteries.
110
W INTER
SOLSTICE
TRANSITION
SUN
Fig. 7-Comparison of predicted and orbital temperatures for oscillator and books.
The second and third satellites built to this
design agree with the first within approximately
2°F, indicating that the design is basically stable
and very reproducible and therefore requires no
individual tailoring.
The use of 16 individual heaters will greatly in-
25
TABLE I
PREDICTED TEMPERATURES OF SATELLITE UNDER VARIOUS ORBITAL CONDITIONS
Nominal
Case
Coldest*
Hott est*
Books*
Batteries* Oscillator*
+39 °
67 ° Avg.
66-68(±I °F )
62.5 ° Avg.
59-66(±2 °F )
80 °
(±5 ° )
-26 °
+44 °
67 ° Avg.
66-68(±I °F )
64.5 ° Avg.
61 - 68(±2 °F )
81 °
(±5°)
-1 3 °
+56 °
69 ° Avg.
68.5- 69.5(±I °F )
68 ° Avg.
67-69(±I °F )
83 °
(.±3 ° )
Sh ell
Baseplate
Sh ell
Baseplate
Sh ell
Baseplate
Minimum Sun,
Magnetic
- 30°
+31 °
- 34 °
+23 °
-24 °
Minimum Sun,
Gravity, I nitial Time
-32 °
+36 °
- 36 °
+28 °
Gravity, Transition
Sun, Initial-Time
- 19 °
+45 °
-22 °
+33 °
Minimum Sun,
G ravity, O ne-Year
D egradation
- 21 °
+48 °
- 25 °
+40 °
-15 °
+56 °
Transition Sun,
O ne-Year D egradation
-
+67 °
-
+59 °
+ 3°
+75 °
Launch,
Spin Stabilized
3°
6°
Shell - 10 ° to +30°, R ad. 10 °_80 °
69.5 ° Avg. 66 .5 ° Avg.
68 .5-70.563-70(±I °F )
(±1.5 °F )
83 °
(±2 ° )
71.0 ° Avg. 69.2 ° Avg.
70.5-71.568-70(±1.5 °F )
(±1.0 °F )
86 °
(±1 0 )
60-90 °
70-105 °
55-85 °
* The
coldest and hottest case conditions account for maximum effects of variations of the solar
constant from 429.3 to 459.0 btu/hr-fe, and the maximum effect of a 10 ° ( 0 to peak ) libration averaged over the orbit. The (± X OF) figures under books, batteries, and oscillator are
the predicted results of this effect.
crease reliability of the temperature control system.
Good heat transfer paths are provided between
components, and failure of one heater will be compensated for by a d jacent units.
The so-called "degraded" cases tested (darkening of the white exterior paint due to ultraviolet
d egradation ) correspond to the maximum value of
degradation expected in one year. Consequently,
the satellite books and batteries will probably be
maintained at temperatures in the range of 65 0 to
75°F for several years. The nearly constant book
and battery temperature w ill also extend the life
of the satellite's memory a nd power system and
should provide an overall long life for the satellite.
M
.
PUBLICA TI O N~ S
The following list is a compilation of recently published
technical articles written by APL stall;. members.
M . H . Friedman, " Shock Tube Measurement of Explosive Sensitivity,"
Combustion and Flame, 10, No.2,
June 1966, 112-119.
M. H. Friedman, "Approximate
Closed Solutions for D etonation
Parameters in Condensed Explosives," AIAA ]., 4, No.7, J uly
1966, 11 8 2-11 8 7.
S. M. Yionoulis, " D etermination of
Coefficients Associated with the
26
Geopotential Harmonic of D egree
and O r der (n,m) = (13, 12 ) ,"
J. Geophys. Res., 7 1, No. 16,
Aug. 15, 1966, 4064.
V . G . Sigilli to, "Pointwise Bounds
for Solutions of the First I nitialBoundary Value Problem for
Parabolic Equations. " Soc . Ind .
Appl. Math. , ]. Appl. Math., 14,
No.5, Sept. 1966, 1038-1056.
R. M . Hanes 2.nd ]. W. Gebhard,
"The Computer's Role in Command D ecision," U.S . Naval I nst .
Pro c., Sept. 1966, 60-68.
L . Monchick (APL ) , R . ]. Munn
( U niversity of Belfast, Ireland ) ,
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APL Technical Digest